# IEEE INFOCOM 2015 SURF A Connectivitybased Space Filling

- Slides: 26

IEEE INFOCOM 2015 SURF: A Connectivity-based Space Filling Curve Construction Algorithm in High Genus 3 D Surface WSNs Chen Wang and Hongbo Jiang Huazhong University of Science and Technology, China {chenwang, hongbojiang}@hust. edu. cn Hong Kong, April 29 th, 2015

Outline Introduction Preliminary SURF Algorithm Performance Evaluation Conclusion 1/24

Outline Introduction Preliminary SURF Algorithm Performance Evaluation Conclusion 2/24

High Genus 3 D Surface WSNs 3/24

Space Filling Curve (SFC) q In mathematical analysis, the space filling curve refers to a curve whose range contains the entire 2 D unit square (or more generally an N-D hypercube). 4/24

SFC Applications in WSNs q Serial Data Fusion [1, 2] The query is successively (i. e. , serially) update from node to node until all nodes in the network are visited. The last node holds the right value of the query. q Path Planning of Mobile Nodes ØLocalization and coverage [3] ØSensor battery recharge [4] ØData collection by the data mules near the sink [5] 5/24

SFC Construction in WSNs Ø X. Ban, M. Goswami, W. Zeng, X. Gu, and J. Gao, "Topology Dependent Space Filling Curves for Sensor Networks and Applications, " in 32 nd IEEE INFOCOM, 2013, pp. 2166 -2174. Ø A. Mostefaoui, A. Boukerche, M. A. Merzoug, and M. Melkemi, "A Scalable Approach for Serial Data Fusion in Wireless Sensor Networks, " Computer Networks, vol. 79, pp. 103 -119, 2015. 6/24

Our Approach q Intuition of SURF 7/24

Our Approach Constructing SFCs in regions before connecting them. 8/24

Outline Introduction Preliminary SURF Algorithm Performance Evaluation Conclusion 9/24

Cut and Genus q A cut is referred to as a disjoint closed simple curve on a connected and orientable surface M. q The genus of M is deﬁned as the maximum number of cuts without rendering M disconnected. genus=1 genus=2 genus=3 10/24

Iso-contour and Reeb Graph q A iso-contour is a connected component of a level set, i. e. a curve whose points have a constant value. q The Reeb graph reveals the evolution of its level set. 11/24

Cut Identiﬁcation q Theorem 1. The Reeb graph of a closed orientable genus-n surface has exactly n loops [6]. q An arc of the Reeb graph of M is a loop-end arc, if it is merged from two different arcs. q Corollary 2. Each loop in the Reeb graph of M corresponds to one loop-end arc. 12/24

Outline Introduction Preliminary SURF Algorithm Performance Evaluation Conclusion 13/24

Proprocessing q Triangulation of the Network [7] q The triangular structure is still denoted by M, with its vertex (node) set V={vi} , and edge set E = { e = (vi, vj) | vj is called the neighbor of vi }. 14/24

Step 1: Contour Construction q Hop count distance → iso-distance contour. q Proposition 3: An iso-distance contour is a connected and closed cycle. 15/24

Step 2: Cut Identiﬁcation (1) Assigning each node with an iso-contour ID. (2) Constructing regions (arcs). (3) Notifing loop-end regions (arcs). (4) Bisecting loop end regions. 16/24

Step 3: Serial Traversal Scheme q The SFC construction follows several cases. 17/24

Outline Introduction Preliminary SURF Algorithm Performance Evaluation Conclusion 18/24

Visual Results of SURF 19/24

Network Coverage 20/24

Coverage v. s. Path Length 21/24

Outline Introduction Preliminary SURF Algorithm Performance Evaluation Conclusion 22/24

Conclusion q We proposed SURF, the ﬁrst solution for the SFC construction in high genus 3 D surface WSNs. Ø It requires connectivity information only, without the reliance on the location or distance measurement. Ø It does not rely on any particular communication model. Ø It is fully distributed and scalable, with a nearly constant storage and communication cost of every node. q A proportional coverage of the generated SFC, with an adaptive density for a given traversal budget or delay constrain will be an interesting direction for the future. 23/24

References 1. S. Patil, S. R. Das, and A. Nasipuri, "Serial Data Fusion Using Space-Filling Curves in Wireless Sensor Networks, " in Proceedings of IEEE SECON, 2004, pp. 182 -190. 2. A. Mostefaoui, A. Boukerche, M. A. Merzoug, et al. , "A Scalable Approach for Serial Data Fusion in Wireless Sensor Networks, " Computer Networks, vol. 79, pp. 103 -119, 2015. 3. J. M. Bahi, A. Makhoul, and A. Mostefaoui, "Localization and Coverage for High Density Sensor Networks, " Computer Communications, vol. 31, pp. 770 -781, 2008. 4. L. Xie, Y. Shi, Y. T. Hou, et al. , "Making Sensor Networks Immortal: An Energy-Renewal Approach with Wireless Power Transfer, " IEEE/ACM Transactions on Networking, vol. 20, pp. 1748 -1761, 2012. 5. R. Sugihara and R. K. Gupta, "Path Planning of Data Mules in Sensor Networks, " ACM Transactions on Sensor Networks, vol. 8, pp. 1: 1 -1: 27, 2011. 6. K. Cole-Mc. Laughlin, H. Edelsbrunner, J. Harer, et al. , "Loops in Reeb Graphs of 2 Manifolds, " in Proceedings of ACM So. CG, 2003, pp. 344 -350. 7. H. Zhou, H. Wu, S. Xia, et al. , "A Distributed Triangulation Algorithm for Wireless Sensor Networks on 2 d and 3 d Surface, " in Proceedings of IEEE INFOCOM, 2011, pp. 1053 -1061. 24/24

IEEE INFOCOM 2015 Thanks for your attentions ! Networked and Communication Systems Research Group (NEST) http: //ei. hust. edu. cn/teacher/hongbo/NEST/index. html